Practical confidence intervals for process capability indices

A process capability index such as C{dollar}sb{lcub}rm pk{rcub}{dollar} quantifies the variability in a process, and can express the capability of a wide variety of processes. Simulations show that one sided confidence intervals for C{dollar}sb{lcub}rm pk{rcub}{dollar} recommended by other researchers are overly conservative. The same simulations indicate that the conservatism results from an error caused by a fundamental logic flaw.; Capability indices derived by univariate noncentral t method are recommended, although they are also slightly conservative. The maximum advantage obtainable from more elaborate methods has been quantified for known parameter values. Equations developed by multiple linear regression procedures are used to predict the minimum value of C{dollar}sb{lcub}rm pU{rcub}{dollar}(or C{dollar}sb{lcub}rm pL{rcub}{dollar}) and the true capability indices for 95% and 90% confidence levels. Performance evaluation shows that these equations are more accurate than published normal approximation methods.; A simulation of capability indices for skewed distributions is conducted and the results are used to compare the noncentral to method with published bootstrap method results. The univariate noncentral t method is comparable in confidence level, but more precise in interval width.